However "Anime" is usually in one section in retail and rental stores, while "Horror", "Action", "Science Fiction", and "Drama" are in seperate sections.

Yea. But guess what's next to it?

Spoiler:

The rest of animation, especially Disney

Animation gets separated because it's a different medium than "movies", which has some overlapping genres. Likewise, Video Games may have similar genres as well - but - the nature of that medium needs its own set of genres, that does not apply to movies and animation. So, having said. The terms "genre" and "medium" -- these two ideas overlap each other like a wire mesh.

Nevertheless, I do not advocate grouping up all animation in a disorganized fashion: like mixing up Spongebob in the "anime" category.